1. Field of the Invention
The present invention relates to techniques for measuring thickness profile and refractive index distribution of multiple layers of thin films by means of two-dimensional reflectometry.
2. Description of the Related Art
The process of measuring thickness profile and associated refractive index distribution of multiple layers of thin films on a substrate as a part of thin film coating process in manufacturing semiconductors, displays such as LCDs and others plays a key role in reducing the process costs by improving quality and screening defective products in early stages of the production cycle through accurate and consistent observation and monitoring of thin film formation process on a substrate.
Widely used apparatus for measuring thickness and refractive index of thin films in semiconductor industry is reflectometry-based measuring tools. In a broad sense, a reflectometer called “Thin Film Layer Measurement System” is a non-contact, non-destructive measuring apparatus, which is capable of measuring the properties of multiple layers of thin films, and also is capable of direct measurement without requiring any special pre-preparation process of target samples prior to measurement.
FIGS. 1a and 1b show a schematic drawing of the structure of a commonly used reflectometer. Referring to FIGS. 1a and 1b, the light generated from a light source 100 is reflected by a beam splitter 102 and passes through an object lens 104 and is directed onto a sample thin film 110 on a sample substrate 108. The sample substrate 108 consists of a substrate 106 and a sample thin film 110 formed on said substrate 106. The light incident onto the sample thin film 110 is partly reflected at the surface 112 of said sample thin film 110, that is, at a point 116 on the boundary 112 between the sample thin film 110 and the air. The rest of the incident light penetrates into said sample thin film 110 and then reflected at the surface 114 of said substrate 106, that is, at the boundary 114 between sample thin film 110 and said substrate 106. This reflected light passes through said object lens 104, said light splitter 102 and through a hole 120 on a reflector 118, and then finally reaches a spectroscope 130, after which the incoming reflected light is detected and analyzed to find the intensity of the reflected light as a function of wavelength. These results are processed by a numeric converter 132 and also by the information processor 134 to compute the thin film thickness and the corresponding refractive index among others.
In the above example in reference to FIG. 1a, the incident light is reflected in part at the point of incidence 116 on the surface 112 (or the boundary 112.) of a sample thin film 110 and the other part passes through the boundary 112 and refracts or penetrates into the sample thin film 110, and in turn this refracted light is reflected in part at the boundary 114 between the sample thin film 110 and the substrate 106 and the rest of the refracted light refracts or penetrates into the substrate 106.
In FIG. 2, two different thin film layers are considered for illustration. Referring to FIG. 2, an incident light 210 that passes through the object lens 104 in FIG. 1a, is reflected in part at a point 217 on the first boundary 207 and the reflected light 222 travels in the direction of 222, and the other part of the incident light 210 refracts into the first thin film layer 202 shown as 212. This refracted light 212, in turn, is reflected at a point 218 on the second boundary 208 and this reflected light travels through the first layer 202 and then to the air in the direction of 224, and the other part of the light 214 refracts into the second thin film layer 204 at a point 218 on the second boundary 208 shown as 214. This refracted light 214 at the point 218, likewise, is reflected at a point 219 on the third boundary 209, and then passes through two layers of thin films 204 and 202, and travels in the air in the direction of 226. Finally, the other part of the reflected light 214 refracts or penetrates in into the substrate 206 in the direction of 216.
As illustrated in FIG. 2, the reflected lights of 222, 224 and 226 from the sample substrate 230, travels in parallel in the air with very small differences in optical paths in terms of absolute point of travel of the reflected lights. In other words, these reflected lights of 222, 224 and 226 travel in parallel in the air seeing from the reference starting line 228 in the air after being reflected at the optical boundaries 207, 208 and 209. As a result, interference phenomena occur. Here, these very small optical path differentials among three reflected lights of 222, 224 and 226 occur as a function of the wavelength of the reflected lights. As a result depending upon the wavelength, the path differentials may cause either mutually re-enforcing interference or mutually canceling interference.
Due to such interference phenomena described above, the plot of reflectivity as a function of wavelength of the reflected light takes a typical form of graph as shown in FIG. 3, whereby the horizontal axis is wavelength and the vertical axis is reflectivity, which is defined as the ratio of the intensity of the reflected light and the incident light intensity.
Referring to FIG. 1a, the reflected light from said sample substrate 108 is a superimposed wave of many wavelengths, thereby it is necessary to find the reflectivity as a function of wavelength, and such wavelength separation takes place in the spectroscope 130. Physically, a prism is a simplest form of a spectroscope, but such wavelength separation is commonly carried out using a diffraction grating to generate monochromatic wavelength. Accordingly, either a monochromator equipped with a rotational type of a diffraction grating and a single light detector on a fixed type of diffraction grating and an array type of light detectors are used for detecting the intensity of the reflected lights as a function of wavelength, thereafter a reflectivity for each wavelength is computed by means of an information processor 134 after transforming the detected reflectance intensity information into numbers by using a numeric converter 132.
The reflectivity graph as shown in FIG. 3, has a unique shape or form depending upon the characteristics of the thin film thickness as well as the refractivity distribution of the thin film and the substrate. In case of a single layer of thin film, the reflectivity is given theoretically as a closed form. However, in case of multiple layers of thin films, the reflectivity can be computed by using the relationship between the electric field and the magnetic field expressed by the products of characteristic matrices, one for each thin film layer. Therefore, the resultant characteristic matrix represents all layers of thin films as a “system”. Unlike in case of a single layer of thin film, whereby the three parameters of refractive index, thin film thickness and reflectivity are related functionally and deterministically, said resultant characteristic matrix for multiple layers of thin film may be rearranged as nonlinear functions, and such nonlinear functions of multiple variables can be “solved” practically, in many cases, by using a method of finding a “best” or an “optimum” solution by means of an iterative trial-and-error method. More specifically, when a reflectivity graph such as the one shown in FIG. 3 is given, for each point of wavelength by choosing the thin film thickness as a variable, selecting its initial value, using such initial value as a starting paint to find a calculated reflectivity by using said nonlinear functional equation, finding an error between the calculated and measured reflectivity values, and then repeating this process iteratively by using different values for the thin film thickness until a value for the thin film thickness that minimizes the error values for the thin film thickness, can be determined, and such values are the “best” estimates for the thickness. Here, the intensity of the incident light for calculating the reflectivity value is determined by using a known sample substrate and light source.
Refractive index is computed from the reflectivity and related information obtained above. Such method is known as a class of “model-based measurement method”. The principle of reflectometry is used to find the thickness of thin films or refractive indices by means of finding a “best” solution using the iterative trial-and-error method described above.
Commonly and widely used reflectometer measures the thin film thickness at a selected “spot” on a production substrate in order to find the uniformity of a given thin film. In order to carry out a measurement, in FIGS. 1a and 1b, through a light-detecting hole 120 of 200 μm in diameter located in the middle of a reflector 118, only a small portion of the reflected light is taken out of the projected image 122, that is, only the reflected light going through the light-detecting hole 120 is used for measuring thin film thickness.
Depending upon the spectroscope used, a glass fiber 424 of 200 μm in diameter as shown in FIG. 4 is used for collecting the reflected lights for measuring thin film thickness. That is, a hole of 200 μm is made on the upper plate 423 in order to accommodate a glass fiber of 200 μm in diameter and as illustrated in FIG. 1b, only the image of the size of 200 μm in diameter is used for measurement out of the entire projected image 122.
On the other hand, a method and apparatus of measuring thickness profile over a large area is disclosed by A. M. Ledger in U.S. Pat. No. 5,333,049. According to Ledge's invention, an apparatus that measures a thickness profile of a silicon wafer as large as 100 mm has been realized using a white light source and the principle of interferometry, whereby the method of measurement is to divide entire wafer into 400 small regions. At each region, reflectivity is measured and compared with an already prepared standard reflectivity vs. thickness table to determine a thickness value at a selected region, whereby said standard reflectivity vs. thickness table is prepared in advance using a calibration wafer and by dividing the scale of thickness into 500 divisions.
In other words, a thickness value is read from a look-up table after measuring a value of reflectivity. This method has advantages of speedy measurement and capability of observing the entire substrate area, but it has also disadvantages of potentially propagating any errors or inaccuracies that many be imbedded in the reflectivity vs. thickness table generated for a calibration substrate to production substrates, and also it has a disadvantage of not being able to obtain sufficient resolution for covering the entire production substrate surface of more than 100 μm in diameter by using the CCD sensors commonly used in video cameras. Here, the problem of resolution arises when a specific part of the electronic circuitry on a substrate is to be inspected during a semiconductor wafer process of high circuit density, because there is a necessity of observing and inspecting thin film thickness and the state of its profile of the surface of a wafer that contains high circuit density. Furthermore, another disadvantage of Ledger's invention is to generate in-situ a new database of reflectivity vs. thin film thickness table of a new calibration substrate whenever the wafer process is changed. Also, another disadvantage of aforementioned Ledger's patent is that the noise contained in the measured reflectivity value of a production substrate reflected in determining thin film thickness value, thereby inaccurate thickness values of the thin film on a calibration substrate is propagated to production substrates. In order to overcome some of these deficiencies, in another U.S. Pat. No. 5,365,340, Ledger disclosed a method of measuring thickness of a thin film by self-normalizing the measured values of reflectivity of a production substrate and comparing these self-normalized values with the values of the database of a calibration substrate, whereby the self-normalization of the measured values of reflectivity is carried out by minimizing the computed values of a merit function. However, all the remaining deficiencies accompanied by the aforementioned U.S. Pat. No. 5,333,049 still apply to U.S. Pat. No. 5,365,340.
The common and serious deficiency shared by aforementioned U.S. Pat. No. 5,333,049 and U.S. Pat. No. 5,365,340 is that the resulting measured values of a thin film thickness are influenced too much by the values of the database of a calibration wafer because the values of a thin film thickness are determined by comparing the measured thickness values with the pre-prepared database by using a calibration substrate. In other words, the reflectivity vs. thin film thickness database of a calibration substrate is simply a table representing a correspondence relationship between the reflectivity and thin film thickness, which table is generated by taking averaged and arranged values over the entire calibration substrate, and therefore, its accuracy is guaranteed when a fair degree of uniformity exists in measured thickness and reflectivity of a calibration substrate as well as production substrates. However, the thin film thickness accuracy decreases when there exist irregular relationships between the reflectivity and the thin film thickness due to the bumpy surface condition of the substrates.
In order to overcome some of the deficiencies described above, Paul J. Clapis and Keith E. Daniell U.S. Pat. No. 5,555,472 disclosed a process of optimally determining the values of a thin film thickness by minimizing the error value between the reflectivity values measured at many points on the surface of a production substrate and the theoretical signatures from a library constructed by computing the values of a signature such as reflectivity using a theoretical numerical expression of the same signature. This method is used for measuring thickness of two layers of thin films under the assumption that at least one layer is reasonably uniform.
Three prior arts described above are about the apparatuses measuring over the entire substrate. Hence, the CCD camera used for measuring a thin film thickness over the entire substrate area has a limited resolution and, in particular, the measurement of a thin film thickness profile in detail over a limited area becomes a serious problem as well as the aforementioned “noise” is introduced in the measuring apparatus and such noise is propagated to production substrates. On the other hand, for example, U.S. Pat. No. 4,999,014, U.S. Pat. No. 4,999,508 and U.S. Pat. No. 4,999,509 disclose methods of determining the values of thin film thickness by “spot” measuring the reflectivity of a thin film on a production substrate. These apparatuses are typical thin film thickness measuring devices utilizing existing spectroscopy and they measure thickness and refractive index of a thin film at a specific point. However, it is generally insufficient to evaluate the property and quality of a thin film with only the measurement information on the thin film thickness and corresponding refractive index at one point. Instead, if the thin film thickness profile and refractive index distribution can be measured over an extended area, such information can be useful in obtaining much more meaningful results in evaluating the property and quality of a thin film rather than the information obtained by measuring at one spot at a time. Furthermore, currently existing spectroscope is unsuitable for measuring thin film thickness profile over a relatively large area or measuring the thin film thickness distribution over many neighboring points at the same time. Of course, it is quite possible to measure the thin film thickness distribution by repeatedly measuring the thickness while moving the sample substrate in four X-Y directions in steps, but such operation requires a fine micro-manipulator and is very time consuming. Moreover, in order to obtain a thin film thickness distribution, a precision substrate moving platform should be used and have a capability of moving with better than 0.1 micron in step resolution, and therefore, the entire measuring apparatus become very complex both functionally and structurally and very expensive. In such a case, it is possible to employ a highly priced super micro-manipulator, but it is not practical from the economic point of view.